Bonding Character of Amino and Cyclopropyl Substituted Six‐Membered Ring Carbenes: DFT/NMR and AIM A

Physical Chemistry Communications, Volume 3 Issue 2, October 2016 www.bacpl.org/j/pcc

Bonding Character of Amino and Cyclopropyl Substituted Six‐Membered Ring Carbenes: DFT/NMR and AIM Analysis Seyed Majid Musavi*, Javad Amani Department of Chemistry, Shahr‐e‐Qods Branch, Islamic Azad University, Shahr‐e‐Qods, 37515‐374, Tehran, Iran Corresponding author, Tel./fax: 98 21 46896519; E‐mail address: moosavi_majid@yahoo.com

Abstract A systematic B3LYP/6‐311++G**//B3LYP/6‐31+G* calculations of GIAO/CSGT‐NMR (σd, σp, σii and ∆χanis) and AIM (



,

  and ε) are performed on some X‐substituted six‐membered ring carbenes (3a/3b, 4a/4b/4c, and 5a/5b; X=amino and 2

cyclopropyl). The findings confirm the interaction of divalent centers with neighboring attached groups, either amino or cyclopropyl, but have a much more pronounced impact for the former. The N–Ccarbene bonds of all singlet carbenes are stronger than their corresponding triplets and the π‐components also bring about higher charge transfer contributions as compared with the corresponding triplets. The large chemical shielding anisotropy at the Ccarbene could mainly be related to a low‐lying n→π* transition, σxx,p. The extent of paramagnetic contribution is generally proportional to the inverse of singlet‐triplet gaps ΔEs‐t.

Calculated 13Ccarbene chemical shifts for singlet states are significantly more downfield as compared with their corresponding triplets. Calculated σiis at the Ccarbene show that the amino and cyclopropyl groups have the same behavior in the polarization of the X–Ccarbene bond toward X, but the amino group has a more π back‐donation ability. In the singlet carbenes, the absolute values of paramagnetic components decrease in the order of σxx,p > σyy,p > σzz,p, but in the triplet carbenes the order is almost reverse. The calculated ∆χanis values show that the electron delocalization to carbene center of all triplet carbenes is less than the corresponding singlet states.

Keywords Six‐membered ring NHCs; 13C NMR; AIM; DFT‐B3LYP

Introduction Divalent carbon species, named carbenes, are important intermediates in organic chemistry [1‐4]. For a long time, this was a popular belief that carbenes are elusive species in the sense that they could only be directly observed by spectroscopic techniques, either in the gas‐phase [5‐9] or in low‐temperature matrices [10‐13], but they could not be isolated in macroscopic amounts at room temperature. Nevertheless, this idea was changed by the syntheses of stable crystalline singlet carbenes (imidazol‐2‐ylidenes 1 with R= adamantyl, aryl or tert‐butyl [14‐16], and imidazolin‐2‐ylidenes 2 with R= aryl [17]), all belong to the N‐heterocyclic carbenes (NHCs) family (Scheme 1).

R

R

N

N

N

N

R 1

R 2

SCHEME 1. TWO STABLE CRYSTALLINE SINGLET NHCS.

The discovery of transition metal complexes of NHCs has paved the way for NHCs to become universal ligands in organometallic and inorganic coordination chemistry. The stability of free NHCs has received much attention [18].

Besides, the experimental researches, the progress of computational chemistry in the last two decades has facilitated the study of such reactive species and has opened new insight into the characterization of different carbene species [19].

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Reported theoretical studies have illustrated some facts around the bonding nature of NHCs. It is known that the stability of free NHCs is mainly attributed to the pπ‐pπ delocalization of adjacent nitrogen atoms [20]. Steric effects are also contributed to the stability of NHCs but in a smaller extent. NHC complexes of almost any main‐group elements and transition metals in a wide variety of oxidation states have been known to date [21]. Most studied stable NHCs have been five‐membered rings, while there are less investigation on the six‐membered ring ones.

In view of our interest in the six‐membered NHCs [22], herein a theoretical study is carried out on the singlet and triplet states of several carbene structures, 3a, 3b, 4a, 4b, 4c, 5a, and 5b (Scheme 2) by concentrating on the 13Ccarbene NMR data to probe the effects of amino and cyclopropyl groups.

N

N

N

3a

N

3b

N

4a

N

N

4b

5a

4c

5b

SCHEME 2. STRUCTURES OF THE SIX‐MEMBERED RING CARBENES UNDER STUDIED.

Moreover, in this manuscript our focus will be on the challenging nature of substituent–Ccarbene interactions and the Ccarbene bonding character [23, 24] using the analysis of the topology of the electron density obtained from theoretical wave functions based on the Bader’s theory of “atoms in molecules (AIM)”.

Computational Details All calculations in this work are performed by the B3LYP‐DFT approach using the Gaussian 03 program package [25]. The B3LYP approach is a hybrid method which includes Becke’s three‐parameter nonlocal exchange potential [26] with the nonlocal correlation functional of Lee, Yang, and Parr [27]. The 6‐31+G* basis set [28] is used for full geometry optimizations and subsequent frequency calculations for both estimation of stationary points as real minima and for inclusion of the ZPE corrections. AIM analyses on optimized structures are accomplished at higher level of DFT (B3LYP/6‐311++G**) employing AIM 2000 program [29]. As well, 13C NMR shielding tensors and chemical shifts (δ, ppm) vs TMS (σC = 178 ppm) are calculated using correlated level of GIAO (gauge including atomic orbitals) [30], CSGT (continuous set of gauge transformations) [31], single origin and IGAIM (a slight variation on the CSGT method)‐B3LYP methods [32, 33] using 6‐311++G** basis set on the B3LYP/6‐31+G* geometries. Finally, single origin, IGAIM and CGST‐B3LYP/6‐311++G** are used for magnetic susceptibility anisotropies (∆χanis) using the B3LYP/6‐31+G* geometries.

Results and Discussion AIM Analysis The AIM theory [34‐37] is a powerful method to analyze molecular structures and makes a link between quantum mechanics and standard chemical concepts, such as an atom and a chemical bond. Despite the wide acceptance and use of AIM by both chemists and physicists, it should be noted that it is a theorem and not a set of proven facts [38].

Chemical bonds between pairs of atoms can be identified by (3,‐1) critical points (also called bond critical points, BCPs) of the charge density ρ(r). In the AIM analysis, critical points (points at which  =0 and (

2

 ) =0) of

electron density distribution are obtained and additional characterization is done using the corresponding Hessian matrix. Diagonalization of this matrix yields the coordinate invariant eigenvalues: λ1 ≤ λ2 ≤ λ3. The quantities including Laplacian, 

78

2

b , of charge density at the bond critical point and ellipticity, ε, are defined as:

Physical Chemistry Communications, Volume 3 Issue 2, October 2016 www.bacpl.org/j/pcc

3

 2 b   i (1) i 1



1  1 (2) 2

The negative Laplacian is an indicator of a covalent bond, whereas a positive Laplacian indicates a non‐covalent interaction. While, the strength of a chemical bond (bond order) is reflected in the electron density at the BCP ρ(r).

The ellipticity describes symmetry of the electron density distribution along the bond path. The bond ellipticity is a measure of the stability where higher values indicate reduced stability of the corresponding bond [39]. In addition, when the λ1 / λ2 ratio is large, an elliptic structure is encountered indicating a large π‐character of the bond and when λ1 = λ2, bond is more cylindrical. The ellipticity can also be used to detect conjugation. In the conjugated systems, the ellipticity value of formal double bonds will slightly tend to decrease whereas single bonds will experience an increase. Similarly, the ellipticity will also change as a result of hyperconjugation which is accompanied by an increase in the ellipticity of the single bonds.

TABLE 1. TOPOLOGICAL PARAMETERS OF THE BOND CRITICAL POINTS (BCPS) FOR THE STUDIED CARBENES AT B3LYP/6‐311++G**.

Structure

BCP

 (au)

 2  (au)

ε

3a (s)

N−Ccarbene

0.312

‐0.676

0.127

3a (t)

N−Ccarbene

0.298

‐0.809

0.237

3b (s)

N−Ccarbene

0.314

‐

‐

3b (t)

N−Ccarbene

0.300

‐0.717

0.172

4a (s)

N−Ccarbene (C−Ccarbene)

0.324 (0.266)

‐0.439 (‐0.651)

0.206 (0.018)

4a (t)

N−C

(C−Ccarbene)

0.299 (0.266)

‐0.763 (‐0.638)

0.231 (0.087)

4b (s)

N−C

(C−Ccarbene)

0.317 (0.272)

‐0.481 (‐0.685)

0.301 (0.000)

4b (t)

N−Ccarbene (C−Ccarbene)

0.297 (0.266)

‐0.676 (‐0.639)

0.281 (0.110)

carbene

carbene

4c (s)

N−Ccarbene (C−Ccarbene)

0.319 (0.269)

‐0.479 (‐0.665)

0.287 (0.010)

4c (t)

N−Ccarbene (C−Ccarbene)

0.308 (0.269)

‐0.672 (‐0.652)

0.316 (0.100)

5a (s)

C−Ccarbene

0.283

‐0.727

0.020

5a (t)

C−Ccarbene

0.271

‐0.661

0.085

0.285

‐0.741

0.028

5b (t)

C−Ccarbene

0.273

‐0.672

0.100

Ethane

C−C

0.242

‐0.547

0.000

Ethene

C−C

0.346

‐1.010

0.374

5b (s)

C−C

carbene

Table 1 summarizes results of the AIM calculations including BCPs of divalent carbons (Ccarbene),  ,  2  and ε for all carbene structures in this study. In addition, for the sake of comparison, the same topological characters are also calculated at the same level of theory for the classical C–C bond in ethane and C=C bond in ethene. Based on AIM context, the negative sign of the Laplacian of electronic charge densities is an indicative of share interactions or covalent bonds which is met in all the N–Ccarbene and C–Ccarbene bonds, however, considering the amounts of the charge density, ρ, in BCPs connecting Ccarbene to the neighboring nitrogen or carbon atoms, the strength of bonds clearly varies. AIM analyses show stronger N–Ccarbene bond for singlet 3a(s) as compared with the corresponding triplet structure 3a(t) (ρ = 0.312 au and 0.298 au, respectively). This result is in accord with the previous findings

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that amino groups stabilize the carbene centers through well‐known σ‐acceptor/π‐donor characters [22]. In other words, according to the resonance arguments, this stabilization occurs via a π‐electron donation from the nonbonding lone pair on the nitrogen atom into the empty p orbital on the Ccarbene. Interestingly, the same results are also found for N–Ccarbene bonds of all singlet and triplet states of the other carbenes, 3b(s) vs. 3b(t), 4a(s) vs. 4a(t), 4b(s) vs. 4b(t), and 4c(s) vs. 4c(t). Moreover, in the series 4a, 4b, and 4c, with two different carbenic bonds, the calculated ρ values obtained for C–Ccarbene bonds are smaller than those of N–Ccarbene bonds and fall within the narrow range of 0.266‐0.272 au. Also, the amounts of ρ values in BCPs connecting carbon atoms to divalent centers of 4a, 4b, 4c, 5a, and 5b are larger than those of C–C single bond in ethane (ρ = 0.242 au) and smaller than those of C=C double bond in ethene (ρ = 0.345 au). These findings confirm the interaction of divalent centers with neighboring attached groups, either amino or cyclopropyl, but much more pronounced for amino group in the singlet states. In the case of cyclopropyl, it is in accord with those expected for bisected W‐shaped conformations (with an antisymmetric Walsh orbital), in which the effective hyperconjugation of a cyclopropyl group with singlet carbene can occur through delocalizing an empty p orbital on an adjacent carbon [40].

Unsaturation decreases the calculated ρ values for N–Ccarbene bonds from 0.324 au in 4a(s) to 0.317 au and 0.319 au in 4b(s) and 4c(s), respectively, which signifies the decrease of the proposed n→p interaction. Furthermore, the ρ values of C–Ccarbene bonds in 5a and 5b are more than those of 4a, 4b, and 4c. Therefore, the C–Ccarbene bonds are stronger in 5a and 5b as compared with those in 4a, 4b, and 4c (Table 1).

More inspection of the Laplacians in Table 1 reveals that while N–Ccarbene bonds of singlet states have higher bond orders as compared with the corresponding triplets, the Laplacian at the N‐Ccarbene BCPs of triplet states are more negative as compared with the singlet states. This opposes to the corresponding trends obtained for the C‐C bonds in ethane (  = 0.242, 

2

 = ‐0.547) and ethene (  = 0.346,  2  = ‐1.010). To justify this finding, one can say that

the π‐component brings about higher charge transfer contributions in the N‐Ccarbene bonds of singlets than those of the triplet states. Therefore, the N‐Ccarbene bonds in singlet states have a substantial ionic contribution and a lower degree of covalent π bonding. This is not the case for the corresponding C‐Ccarbene bonds. Also, in the singlet states 4a‐c, the N–Ccarbene bonds have higher covalent bond orders as compared with the corresponding C‐Ccarbene bonds, but the Laplacian of the former is less negative as compared with the latter. This is not the case for the corresponding bonds in the triplet carbenes. Thus, the N‐Ccarbene bonds in the singlet carbene structures are characterized by a partial ionic contribution and a lower degree of covalent π‐bonding as compared with a typical C=C double bond in ethene. This result is in good agreement with that previously obtained for the synthesized stable singlet Arduengo type NHCs by Apeloig et al. [41].

NMR Studies Measurement of NMR chemical shift anisotropy at the carbene center is more easily accomplished and provides information that also confirms the highly anisotropic nature of the electron distribution around the carbene center.

There are three principal effects which control NMR chemical shifts: diamagnetic, paramagnetic and neighboring group anisotropy. For the sake of comparison, 13C NMR shielding tensors and chemical shifts vs TMS (σC = 178 ppm) of the Ccarbene centers in 3a‐5b are calculated using four different methods (GIAO, CSGT, single gauge, and IGAIM). The results obtained through CSGT and IGAIM appear very similar, hence the results of less popular method IGAIM are removed from the text. While results of single gauge method appear very distant from other results, a rather good consistency is observed among data from two remaining methods GIAO and CSGT. Nevertheless, despite the absolute numerical values, the trends of data appear consistent among all calculation methods. Considering the chemical shift values for carbene centers in these seven structures, 3a‐5b, it is evident that all singlet states are significantly downfield (more than 100 ppm) as compared with their corresponding triplet states (Table 2). Interestingly, these changes become more pronounced in the lack of amino substituents. The order of the differences between δ13Ccarbene of singlet and triplet states (∆δ13Cs‐t, GIAO) is as follows: 5a (461.4ppm) > 5b (442.4ppm) > 4b (232.6ppm) > 4a (215.8ppm) > 4c (211.3ppm) > 3b (136.2ppm) > 3a (130.8ppm).

The calculated chemical shifts for Ccarbene show that upon substitution of one of the amino groups in 3a and 3b by cyclopropyl (4a, 4b and 4c), a clear downfield shift is found (around 80.3‐86.3 ppm) (Table 2). However, the substitution of both amino groups in 3a and 3b by cyclopropyl is accompanied by further downfield shifts, (4a→5a = 243.7 ppm, 4b→5b = 212.6 ppm, and 4c→5b = 216.2 ppm). To investigate the origin of these shifts upon substitution, the 13Ccarbene magnetic isotropic shielding constants (σ) are split into paramagnetic (σp) and diamagnetic

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(σd) contributions (Table 3).

TABLE 2. CALCULATED CHEMICAL SHIFTS (PPM), MAGNETIC SUSCEPTIBILITY ANISOTROPIES ∆ΧANIS (PPM CGS) AND THE SINGLET‐TRIPLET GAPS ΔES‐T (KCAL/MOL).A

Structure

b iso

δ

3a (s)

247.3

‐109.9, ‐5.2

3a (t)

116.5

‐96.1, 11.7

c

∆χanis

3b (s)

255.3

‐104.5, ‐15.7

3b (t)

119.1

‐84.7, 3.4

4a (s)

327.6

‐98.6, ‐12.2

4a (t)

111.8

‐78.4, 12.8

4b (s)

341.6

‐88.8, ‐20.5

4b (t)

109.0

‐98.6, 3.7

4c (s)

338.0

‐88.1, ‐17.8

4c (t)

126.7

‐74.1, ‐2.2

5a (s)

571.3

‐91.9, ‐20.0

5a (t)

109.9

‐74.0, 15.7

5b (s)

554.2

‐82, ‐27.2

5b (t)

111.8

‐98.1, ‐5.3

∆δs‐t

ΔEs‐t [22]

130.8

60.9

136.2

63.3

215.8

43.3

232.6

43.1

211.3

40.2

461.4

14.8

442.4

17.9

d

All calculations performed at the GIAO B3LYP/6‐311++G**//B3LYP/6‐31+G* level of theory.

The calculated chemical shifts refer to TMS: δGIAO = δTMS ‐ δ, with δTMS = 178 ppm at the same level of theory. c ∆χanis (∆χ = χzz‐ 0.5(χxx + χyy) at single guage‐B3LYP/6‐311++G**//B3LYP/6‐31+G* and CSGT‐B3LYP/6‐311++G**// B3LYP/6‐31+G* (in italics). d δiso, singlet ‐ δiso, triplet a

b

TABLE 3. DIAMAGNETIC (ΣD) AND PARAMAGNETIC (ΣP) CONTRIBUTIONS (PPM) TO THE 13CCARBENE MAGNETIC ISOTROPIC SHIELDING CONSTANT (Σ) AND THE CHEMICAL SHIFT TENSOR COMPONENTS, ΣII, OF THE SINGLET AND TRIPLET CARBENES THROUGH GIAO.

Carbene

σd

σp

σ

σxx

σyy

σzz

3a (s)

253.9

‐323.2

‐69.3

‐281.6

‐32.2

106.1

3a (t)

261.6

‐200.1

61.5

151.1

13.3

20.2

3b (s)

260.2

‐337.5

‐77.3

‐290.8

‐46.0

104.8

3b (t)

260.0

‐201.1

58.9

89.1

42.6

45.0

4a (s)

261.9

‐411.5

‐149.6

‐475.6

‐90.7

117.3

4a (t)

259.0

‐192.8

66.2

159.9

22.4

16.4

4b (s)

282.8

‐446.4

‐163.6

‐505.6

‐102.2

117.0

4b (t)

266.9

‐197.9

69.0

140.9

44.8

21.4

4c (s)

268.4

‐428.4

‐160.0

‐481.8

‐119.3

121.2

4c (t)

258.7

‐207.4

51.3

101.2

29.9

22.8

5a (s)

262.0

‐655.3

‐393.3

‐1054.1

‐261.1

135.3

5a (t)

259.3

‐191.2

68.1

200.1

5.5

‐1.3

5b (s)

270.1

‐646.3

‐376.2

‐987.5

‐280.0

138.7

5b (t)

256.2

‐190.0

66.2

194.9

23.7

‐20.1

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The results show that the substitution of the amino group by cyclopropyl gives no impressive changes in the diamagnetic contribution (σd) and the values are approximately unchanged. But the paramagnetic component values are of opposite sign and show a larger variation. Thus, evidently the differences in the chemical shifts are almost exclusively due to the paramagnetic contribution. The computed chemical shift tensors are collected in Table 3 for the seven carbene structures at their singlet and triplet states. The orientation of the chemical shift tensor at the carbene center is shown in Fig. 1.

FIG. 1. TENSOR COMPONENT ORIENTATIONS AT THE CARBENE CENTER (X = AMINO OR CYCLOPROPYL).

The data in Table 3 show that in these carbenes the tensor σxx values are the most deshielded component whereas the σzz values are the most shielded one. The dependence of the Ccarbene chemical shift on the substituents in carbenes 3a, 3b, 4a, 4b, 4c, 5a, and 5b (Scheme 2) can be explained in terms of the tensor component of the diamagnetic and paramagnetic shielding tensors which are shown in Table 4. The diamagnetic components are all positive and almost do not show an orientation dependence. In contrast, the paramagnetic components are of opposite sign and show larger variations. In the singlet carbenes, the absolute values of paramagnetic components decrease in the order of σxx,p > σyy,p > σzz,p, but in the triplet carbenes the order is almost reverse.

TABLE 4. GIAO‐B3LYP/6‐311++G**//B3LYP/6‐31+G* CALCULATIONS OF THE PARAMAGNETIC, ΣII,P, AND DIAMAGNETIC, ΣII,D, COMPONENTS OF THE CHEMICAL SHIFT TENSOR FOR SINGLET AND TRIPLET CARBENES.

Carbene

σxx,d

σyy,d

σzz,d

σxx,p

σyy,p

σzz,p

3a (s)

283.7

256.2

221.9

‐565.3

‐288.4

‐115.8

3a (t)

272.1

266.3

246.4

‐121.0

‐253.0

‐226.2

3b (s)

282.3

262.9

235.4

‐573.1

‐308.9

‐130.6

3b (t)

274.9

249.2

255.8

‐185.8

‐206.6

‐210.8

4a (s)

306.5

239.2

239.9

‐782.1

‐329.9

‐122.6

4a (t)

281.8

248.9

246.3

‐121.9

‐226.5

‐229.9

4b (s)

322.8

255.8

269.8

‐828.4

‐358.0

‐152.8

4b (t)

287.2

253.2

260.4

‐146.3

‐208.4

‐239.0

4c (s)

313.5

248.0

243.7

‐795.3

‐367.3

‐122.5

4c (t)

278.4

246.3

251.5

‐177.2

‐216.4

‐228.7

5a (s)

299.1

235.2

251.7

‐1353.2

‐496.3

‐116.4

5a (t)

285.3

240.5

252.0

‐85.2

‐235.0

‐253.3

5b (s)

311.1

236.1

263.0

‐1298.6

‐516.1

‐124.3

5b (t)

289.1

243.2

236.2

‐94.2

‐219.5

‐256.3

The σzz,p component is produced by rotation of the nonbonding lone pair of the Ccarbene into the occupied X–Ccarbene bonds. This is a combination of two doubly occupied orbitals which is repulsive, so the resulting magnetic field is small. The combination is in the xy plane and consequently the resulting magnetic field is oriented along the z axis

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(Fig. 1). The magnitude of σzz,p associates with the electronegativity of the atoms bonding to the Ccarbene. The larger the electronegativity is, the more the X–Ccarbene bond is polarized toward substituents X. Therefore, the electron density near Ccarbene and consequently the repulsion between X–Ccarbene sigma bond and the carbene lone pair is reduced. This is accompanied by an increase in the magnetic filed in the z direction. According to Table 4, the values of σzz,p in 3a, 4a, and 5a are approximately constant. So, the amino and the cyclopropyl groups have the same behavior in the polarization of the X–Ccarbene bond toward substituents X. The σyy,p component results from the rotation of X–Ccarbene sigma bond electron density into the empty p orbital on the Ccarbene. This electronic current is in the xz plane and the consequential magnetic field is oriented toward the y axis (Fig. 1). In comparison with the σzz,p, in this electronic current a doubly occupied orbital with an empty p orbital are mixed, so there exists no repulsion. Therefore, the magnetic field in the y direction is supposed to be larger than that in the z direction. The magnitude of this magnetic field correlates with the electronegativity of X. By increasing the electronegativity, the amount of the magnetic field decreases due to the fewer electrons around the Ccarbene. Also, the amount of π back‐donation from X to empty p orbital affects the resulting magnetic field. The magnetic field decreases by more π back‐donation. Comparison of the absolute value of σyy,p (ppm) for Ccarbene in 3a, 4a, and 5a reveals an increase in the σyy,p as follows: 3a (‐288.4) < 4a (‐329.9) < 5a (‐496.3). As mentioned above, the amino and cyclopropyl groups have the same polarization effects. Consequently, this difference demonstrates that the π back‐donation ability of amino group is more than that of the cyclopropyl group.

The absolute values of σxx,p follow the same trend as the σyy,p component, σxx,p(5a) > σxx,p(4a) > σxx,p(3a), but the range of values extends from ‐565.3 to ‐1353.2 ppm, a significant increased variation relative to σyy,p component. The σxx,p component relates the high density of the carbene in‐plane lone pair with the formally unoccupied p orbital at the carbene center. Electron density is readily moved from the carbene lone pair to the out of plane p orbital effectively and creates a magnetic vector perpendicular to the yz plane. This tensor component lies in the plane of the molecule (Fig. 1). In fact, this paramagnetic tensor originates from the circulation of electrons moving between their ground state and excited state orbitals. Qualitatively, this paramagnetic shielding is inversely proportional to the energy gap between the occupied and excited‐state orbitals and depends on the inverse cube of the electrons’ distance from the nucleus as they rotate [42]. The second factor affecting the magnitude of this component is the electron density in the out‐of‐plane p orbital due to π donation of substituents. A vacant p orbital would generate the largest electric field and the largest σxx,p value. Moreover, if cyclopropyl group is substituted for one of the amino groups in 3a and 3b or the amino group in 4a, 4b, and 4c, the corresponding singlet‐triplet gap (ΔEs‐t) becomes smaller (Table 2). Therefore, as shown in Table 4, the largest value of σxx,p is found for 5a with the smallest amount of ΔEs‐t (14.8 kcal/mol) and a less π donation to the empty p orbital on the carbene center. On the other hand, the smallest value of σxx,p is for 3a which has both the largest ΔEs‐t (60.9 kcal/mol) and the most electron density in the p orbital.

The calculated σxx,p and σyy,p for 3a, 4a, and 5a show that if a cyclopropyl group is substituted for one of the amino groups in 3a, the σxx,p and σyy,p values increased by 216.8 and 41.5 ppm, respectively. When the second amino group is substituted by the cyclopropyl group (5a), σxx,p and σyy,p increased to a more extent (571.1 and 166.4 ppm , respectively). The same trend is observed for 3b, 4b, 4c, and 5b. This means that the substitution of the first nitrogen atom does not have the same effect as the second one. It clarifies that the π donation effect of two amino groups is not two times as much as the effect of one amino group. This is also confirmed by the ρ values in Table 1.

The ρ value of N−Ccarbene bond in 4a (s) is higher than 3a (s) implying the more effective interaction of the divalent center with the neighboring amino group in the former.

Comparison of the σxx,p values (ppm) of the carbenic carbon for the identically substituted carbenes, 3a and 3b reveals an increase in the σxx,p absolute values as follows: 3a (‐565.3) < 3b (‐573.1) (Table 4). Also, the similar increase in the σyy,p values is observed. According to Table 2, the existence of C=C bonds in 3b leads to the increase of singlet‐triplet gap, but unexpectedly the value of σxx,p is increased. A decrease of the p orbital electron density of the divalent carbon as a result of a conjugative interaction of nitrogen with the neighboring C=C bond seems to be the main reason for this behavior. As a result, the π donation aptitude of the amino group is diminished and consequently n→π* transition and also rotating the C‐X sigma bond electron density into the empty p orbital increased.

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The absolute values of σxx,p decrease on going from 5a to 5b (‐1353.2 and ‐1298.6 ppm, respectively), but the changes of σyy,p have a reverse trend to those of σxx,p (Table 4). In 5b, there is an interaction between the cyclopropyl ring and the double bond. This conjugative interaction comes from the π orbital of the unsaturated bond and the σ (Walsh‐type) orbitals of the ring. Such an interaction reduces the electron donation from the Walsh‐type orbitals to the empty p orbital of the divalent center. The possibility for this type of interaction has been shown by Heilbronner and co‐workers [43]. There is a net electrons transferring from the cyclopropyl ring to the conjugated double bond and the existence of this electron flow has experimentally been demonstrated by Harada et al. [44].

The increase of σyy,p through the sequence 5a → 5b is in accord with the conjugative interaction as noted above.

According to Table 2, the singlet‐triplet gap in 5b is more than that in 5a; and the difference between these gaps is approximately the same as 3a and 3b. In contrast to 3a and 3b, the interaction of the cyclopropyl groups with the double bonds can not compensate for the effect of singlet‐triplet gap increasing and hence the σxx,p is decreased in 5b.

Finally, in the discussion of magnetic susceptibilities, the significant anisotropy of the magnetic susceptibility, ∆χanis, is regarded as an indication of a ring current and a cyclic electron delocalization. In this basis, from the data in Table 2, one can conclude that the electron delocalization of all triplet state carbenes are less than singlet states due to their smaller negative ∆χanis at CSGT method. Interestingly, the most electron delocalization is observed in the singlet 5b (∆χanis= ‐27.2 ppm cgs) where the strong π donor substituent (X= amino) is replaced by the weak π donor substituent (X= cyclopropyl). While the NMR results of CSGT method are more reliable, disagreement between ∆χanis results of single gauge and CSGT method is observed for the two carbenes, 5b and 4b. In line with our previous results based on isodesmic, NBO, and structural data [22], delocalization of electrons to carbene center is restricted in the presence of two amino groups versus one amino group (∆χanis 3a (s) and 4a (s) are ‐5.2 and ‐12.2 ppm cgs, respectively).

Conclusions High level DFT study of AIM and NMR is performed on seven cyclic carbenes 3a, 3b, 4a, 4b, 4c, 5a, and 5b. The AIM analyses indicate that the N–Ccarbene bonds of all singlet states are stronger than their corresponding triplets and generally the C–Ccarbene bonds are weaker as compared with N–Ccarbene bonds. Calculated 13C chemical shift values of singlet carbene centers are drastically downfield as compared with their corresponding triplet states (more than 100 ppm). The study of chemical shielding tensors at the carbene center demonstrates that the amino and the cyclopropyl groups have the same behavior in the polarization of the X–Ccarbene bond toward substituents X (X = amino or cyclopropyl group), but the amino group has more π back‐donation ability as compared with cyclopropyl group. The largest value of σxx,p is found for 5a which has the smallest amount of ΔEs‐t and less π donation to the empty p orbital on the carbene center and the smallest one for 3a which has both the largest ΔEs‐t and the most electron density in the p orbital. In contrast to 3a and 3b, the interaction of the cyclopropyl groups with the double bonds can not compensate for the effect of ΔEs‐t increasing and hence the σxx,p decreased in 5b. The calculated ∆χanis values show that the electron delocalization of all triplet carbenes is less than the corresponding singlet states.

ACKNOWLEDGMENTS

We are thankful to the Research Council of the Islamic Azad University‐Shahre Qods Branch.

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